As long as the three
Hilbert spaces (REF ) have to
share the same linear
ket-vector-space
component \({\cal V}\)  (cf. Ref. [1]}),
it is necessary to individualize, by the notation,
the respective duals \({\cal V}^{\prime }\) , i.e., the respective invertible antilinear correspondences
(we will write \({\cal T}: {\cal V} \rightarrow {\cal V}^{\prime }\) ).
It would be insufficient to use the same Dirac-recommended
bra-vector symbol \(\langle \chi |\) 
for the denotation of the elements of all
of the different dual spaces
of our interest.
